The sequences of antibodies from a given repertoire are highly diverse at few sites located on the surface of a genome-encoded larger scaffold. The scaffold is often considered to play a lesser role than highly diverse, non-genome-encoded sites in controlling binding affinity and specificity. To gauge the impact of the scaffold, we carried out quantitative phage display experiments where we compare the response to selection for binding to four different targets of three different antibody libraries based on distinct scaffolds but harboring the same diversity at randomized sites. We first show that the response to selection of an antibody library may be captured by two measurable parameters. Second, we provide evidence that one of these parameters is determined by the degree of affinity maturation of the scaffold, affinity maturation being the process by which antibodies accumulate somatic mutations to evolve towards higher affinities during the natural immune response. In all cases, we find that libraries of antibodies built around maturated scaffolds have a lower response to selection to other arbitrary targets than libraries built around germline-based scaffolds. We thus propose that germline-encoded scaffolds have a higher selective potential than maturated ones as a consequence of a selection for this potential over the long-term evolution of germline antibody genes. Our results are a first step towards quantifying the evolutionary potential of biomolecules.